Accelerating the solution of linear systems appearing in two-phase reservoir simulation by the use of POD-based deflation methods

We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed method depends on the number of deflation vectors. The POD-based deflation method is tested for a particular problem and linear solver; nevertheless, it can be applied to various transient problems, and combined with multiple solvers, e.g., Krylov subspace and multigrid methods.

     

Data requirements for a 5-mm quasi-geoid in the Netherlands

We assess the surface gravity data requirements for a 5-mm quasi-geoid model for the Netherlands mainland and continental shelf in terms of omission and commission errors. The omission error critically depends on the roughness of the topography and bathymetry. For the Netherlands continental shelf, Central and Northern Netherlands, the omission error is well described by the model 0.32d mm, where d is the data spacing in km. For the more hilly Southern Netherlands, the omission error model is 0.92d mm. The commission error depends on the kernel modification, the data spacing, and the data accuracy. When using the spheroidal Stokes kernel, it is well described by 0.277 d σ_Δg mm, where σ_Δg is the noise standard deviation of surface gravity data in mGal. An upper bound of the commission error of the state-of-the-art satellite-only gravity model GOCO05S over the Netherlands is e^{0.03676L–11.419} mm, where L is the maximum degree up to which this model is used. Only if this model is truncated at a sufficiently low degree, e.g., at degree 100, its contribution to the total commission error can be neglected. We determine the total error as the sum of commission and omission errors. Hence, to realize a 5-mm quasi-geoid model for the Netherlands mainland and continental shelf, a data spacing of 3.5 km is needed when assuming a noise standard deviation of 1.5 mGal for surface gravity data. The currently available land-based gravity data fulfill this requirement. This does not apply to the situation at sea, where the density of the shipboard gravity data and the accuracy of the radar altimeter-derived data do not allow the realization of a 5-mm quasi-geoid model.     

Spatial mapping of drought in Zambia using regional frequency analysis

Regional frequency analysis based on L-moments was applied to assess the spatial extent of meteorological droughts in tandem with their return periods in Zambia. Weather station monthly rainfall data were screened to form homogeneous sub-regions-, validated by a homogeneity criterion and fitted by a generalized extreme value distribution using goodness-of-fit test statistics. Predictor equations at regional scale for L-moment ratios and mean annual precipitation were developed to generate spatial maps of meteorological drought recurrences. The 80% of normal rainfall level and two thresholds of 60% and 70% were synonymous with moderate and severe droughts, respectively. Droughts were more severe in the south than in the north of Zambia. The return periods for severe and moderate droughts showed an overlapping pattern in their occurrence at many locations, indicating that in certain years droughts can affect the entire country. The extreme south of Zambia is the most prone to drought.     

Magmatism at continental passive margins inferred from Ambient‐Noise Phase‐velocity in the Gulf of Aden

Non‐volcanic continental passive margins have traditionally been considered to be tectonically and magmatically inactive once continental breakup has occurred and seafloor spreading has commenced. We use ambient‐noise tomography to constrain Rayleigh‐wave phase‐velocity maps beneath the eastern Gulf of Aden (eastern Yemen and southern Oman). In the crust, we image low velocities beneath the Jiza‐Qamar (Yemen) and Ashawq‐Salalah (Oman) basins, likely caused by the presence of partial melt associated with magmatic plumbing systems beneath the rifted margin. Our results provide strong evidence that magma intrusion persists after breakup, modifying the composition and thermal structure of the continental margin. The coincidence between zones of crustal intrusion and steep gradients in lithospheric thinning, as well as with transform faults, suggests that magmatism post‐breakup may be driven by small‐scale convection and enhanced by edge‐driven flow at the juxtaposition of lithosphere of varying thickness and thermal age.     

Long-term Field Observations on Seasonality in Chlorophyll-<Emphasis Type="Italic">a</Emphasis> Concentrations in a Shallow Coastal Marine Ecosystem,the Wadden Sea

Analyses of long-term field observations (1974–2007) on chlorophyll-a concentrations in the western Wadden Sea showed no long-term trends in the timing of the wax and wane of phytoplankton spring blooms. There is weak evidence, however, that the height of the autumn bloom has decreased since the early 1990s. This fading of the autumn bloom may have had consequences for the carbon transfer to higher trophic levels, currently hampering primary consumer species that mostly rely on food supply during late summer. Current and other findings suggest a shortening of the growing season due to the fading of the autumn bloom in the Wadden Sea and a lengthening of the growing season due to an advancement of the spring bloom in the North Sea. These regionally different changes in seasonality may have contributed to the coinciding decrease in bivalve filtering capacity in the western Wadden Sea and the large-scale offshore shift of juvenile plaice from the Wadden Sea to the adjacent North Sea.     

Impulsive phase heating and a coronal explosion in a solar flare

The flare of 12 November 1980, 0250 UT, in Active Region 2779 (NOAA classification) was studied by using X-ray images obtained with the Hard X-Ray Imaging Spectrometer aboard NASA's Solar Maximum Mission. In a ten-minute period, between about 0244 and 0254 UT, some five short-lived impulsive bursts occurred. We found that the so-called hard bursts ( 15 keV) are also detectable in low energy images. During that 10 min period - the impulsive phase - the heat input into the flare and the total number of energetic electrons increased practically exponentially, to reach their maximum values at 0254 UT. At the end of that period, when the thermal energy content of the flare was largest, a burst was observed, for the first time, to spread in a broad southern direction from an initially small area with a speed of about 50 km s^–1. We have called this phenomenon a coronal explosion.Fokker Aircraft Industries, Schiphol, The Netherlands.     

Macro-and micro-turbulent filter functions for weak lines in stellar atmospheres

Following a similar discussion given earlier for the solar case (De Jager, 1972) we compute in this paper spectral line profiles for the spatial wavelengths in which a stellar motion field can be decomposed, and thereafter the macro-and micro-turbulent filter functionsf _M(k) andf (k), where is the optical scale height andf ²(k) dk the fraction of the energy of the turbulent motions between wavenumbersk andk+dk of the spectrum of turbulence that contributes to either kind of turbulence. If micro-and macro-turbulent velocity components are known for a certain star, and if the spectrum of turbulence is sharp enough, the ratiof _M/f would enable one to derive the average size of the turbulent elements in the star's atmosphere. The computations apply to weak lines in idealized stellar atmospheres, and refer to two cases: isotropic turbulence, and radial pulsations. These filters can be suitably used in a diagnostic method for the analysis of the motion field in the solar and stellar atmospheres. Some examples of applications to stars of very different kinds are given.     

A dynamo scenario

In this paper, the term dynamo refers to the complex of physical mechanisms that cause solar magnetic activity in all its manifestations. Properties of that dynamo are inferred from observational indications to fit them into a scenario. Properties and models of the manifestations of strong magnetic field are briefly summarized, together with their formation during the emergence of -shaped loops from the toroidal flux system in the interface below the convection zone. The evolution of magnetic concentrations and the flux removal from the atmosphere, with indications for flux retraction, are considered. Then the weak (INF) fields are discussed, together with the role of upward floating LI- shaped loops in the removal of toroidal flux. Finally features of strong and weak fields are fitted into a scenario for a cyclic dynamo, in which the regeneration of the poloidal field of proper sign relies on the cancellation of magnetic flux in the surface transport interpreted as reconnection, followed by retraction of reconnected loops.Dedicated to Cornelis de JagerBased on an invited talk during Solar Cycle Workshop, March 28–30, 1996, Tucson.